Unfortunately this mission "ACA - Weaponry Store" is not working as intended at the moment. Here is what you need to do at the moment to be able to finish the mission, it will work as intended after the patch next week so this is just a temporary workaround. First, you can't have any items equipped, so please unequip all items first. When you are at the Weaponry Store close to the NPC behind the counter, press Y(default) to open up the Action Library. When you have the Action Library opened search for "Select Next Target" then when you found that click on it and it will take you to page 12 where you find the symbol again, press it until the NPC is marked (you might have to click more then once). Then click back to the front page of the Action Library by clicking the large bookmark to the left, then search for "Operate" and click that so it takes you to page 3 in the Action Library. Once you locate "Operate" icon on that page click it and the NPC will talk to you and you can continue your mission from here. You will also have to follow these steps at the Armoury and the Clothing Store. Also remember you can't have any items equipped, so please unequip all items first. And special thanks to Lizbelle for her part in the solution.
The weapon store NPC is fully accessible again with mouse, thank you A-Team! Just posting this since someone visiting Ark just asked me if weapon store was still broken.